<https://databank.worldbank.org/source/world-development-indicators>
Observation 1: Be clear and precise in the explanation and please don’t include nonsense arguments.
Yes. It is possible that the exports or imports can be greater than GDP. This can happen because exports or imports can include intermediate goods. A “toy” example can be found in Oliver Blanchard (2017) Macroeconomics (7 Edition) > Chapter 17 > Openness in Goods and Financial Markets > 17.1 Openness in Goods Markets > Exports and Imports > Can Exports Exceed GDP? and a real example is the case of Singapore:
http://www.banrep.gov.co/ > Estadísticas > ¡NUEVO! Estadísticas Banrep > Tasas de cambio y sector externo > Tasas de cambio nominales > Tasa Representativa del Mercado (TRM) > Diaria > DESCARGAR > Descargar datos en Excel
| Date | Price Big Mac Colombia | Price Big Mac USA |
|---|---|---|
| 2004-05-01 | 6500 | 2.900000 |
| 2005-06-01 | 6500 | 3.060000 |
| 2006-05-01 | 6500 | 3.100000 |
| 2007-01-01 | 6900 | 3.220000 |
| 2007-06-01 | 6900 | 3.410000 |
| 2008-06-01 | 7000 | 3.570000 |
| 2009-07-01 | 7000 | 3.570000 |
| 2010-01-01 | 8200 | 3.580000 |
| 2010-07-01 | 8200 | 3.733333 |
| 2011-07-01 | 8400 | 4.065000 |
| 2012-01-01 | 8400 | 4.197220 |
| 2012-07-01 | 8600 | 4.327500 |
| 2013-01-01 | 8600 | 4.367396 |
| 2013-07-01 | 8600 | 4.556667 |
| 2014-01-01 | 8600 | 4.624167 |
| 2014-07-01 | 8600 | 4.795000 |
| 2015-01-01 | 7900 | 4.790000 |
| 2015-07-01 | 7900 | 4.790000 |
| 2016-01-01 | 7900 | 4.930000 |
| 2016-07-01 | 8900 | 5.040000 |
| 2017-01-01 | 9900 | 5.060000 |
| 2017-07-01 | 9900 | 5.300000 |
| 2018-01-01 | 10900 | 5.280000 |
| 2018-07-01 | 11900 | 5.510000 |
| 2019-01-01 | 11900 | 5.580000 |
| 2019-07-09 | 11900 | 5.740000 |
| 2020-01-14 | 11900 | 5.670000 |
| 2020-07-01 | 11900 | 5.710000 |
| 2021-01-01 | 12950 | 5.660000 |
Observation 1: Be clear and precise in the explanation and please don’t include nonsense arguments.
The uncovered interes parity relation represents a situation where the yield of a national financial product is equal to the yield of a financial product from the rest of the world. In order for residents to have both domestic and foreign financial products in an economy, the yield between both types of financial products must be equal and that represents the uncovered interest parity relation. This condition is consistent with the Balance of Payments of many countries like Colombia where individuals have both national financial products and financial products from the rest of the world.
If a resident in Colombia has to decide to invest between a financial product from Colombia or the USA, then he should compare the yield of these products. If \(i_t\) is the interest rate of the financial product from Colombia then the yield is \(1+i_t\). Also if \(i_t^*\) is the interest rate of the financial product from USA he must first convert his pesos into US dollars to buy the product and then convert the yield he receive in US dollars into pesos. Therefore, the yield of the financial product from USA is \((1+i_t^*)\frac{E_{t+1}^e}{E_t}\). In that way, the uncovered interest parity relation is:
\[(1 + i_t) = (1 + i_t^*)\frac{E_{t+1}^e}{E_t}\] The difference between the condition pointed out in point 9 and the above expression is how the nominal exchange rates, \((E_{t+1}^e, E_t)\), are included. If the nominal exchange rate is expressed as \(\frac{pesos}{1\; dollar}\) then \(E_{t+1}^e\) would be in the numerator and \(E_t\) in the denominator.
This exercises is taken from:
Oliver Blanchard (2017) Macroeconomics (7 Edition) > Chapter 18 The Goods Market in an Open Economy > Questions and Problems > Exercise 8
\[\widehat{C}_t = 10 + 0.8(\widehat{Y}_t - \widehat{T}_t)\]
\[\widehat{I}_t = 10\]
\[\widehat{G}_t = 10\]
\[\widehat{T}_t = 10\]
\[\widehat{IM}_t = 0.3\widehat{Y}_t\]
\[\widehat{X}_t = 0.3\widehat{Y}_t^*\] where \(\widehat{Y}_t^*\) denotes foreign output.
\[\begin{split} \widehat{Y}_t & = \widehat{Z}_t \\ \widehat{Y}_t & = \widehat{C}_t + \widehat{I}_t + \widehat{G}_t + \widehat{X}_t - \widehat{IM}_t \\ \widehat{Y}_t & = 10 + 0.8(\widehat{Y}_t - \widehat{T}_t) + \widehat{I}_t + \widehat{G}_t + 0.3\widehat{Y}_t^* - 0.3\widehat{Y}_t \\ \widehat{Y}_t & = 10 + 0.8(\widehat{Y}_t - 10) + 10 + 10 + 0.3\widehat{Y}_t^* - 0.3\widehat{Y}_t \\ \widehat{Y}_t & = 22 + 0.8\widehat{Y}_t - 0.3\widehat{Y}_t + 0.3\widehat{Y}_t^* \\ \widehat{Y}_t & = \frac{1}{1 - 0.8 + 0.3}(22 + 0.3\widehat{Y}_t^*) \\ \widehat{Y}_t & = 44 + 0.6\widehat{Y}_t^* \end{split}\] Where \(\frac{1}{1 - 0.8 + 0.3} = \frac{1}{0.5} = 2 > 1\) is the multiplier for the domestic economy.
\[\widehat{C}_t^* = 10 + 0.8(\widehat{Y}_t^* - \widehat{T}_t^*)\] \[\widehat{I}_t^* = 10\]
\[\widehat{G}_t^* = 10\]
\[\widehat{T}_t^* = 10\] \[\widehat{IM}_t^* = 0.3\widehat{Y}_t^*\]
\[\widehat{X}_t^* = 0.3\widehat{Y}_t\]
\[\begin{split} \widehat{Y}_t^* & = \widehat{Z}_t^* \\ \widehat{Y}_t^* & = \widehat{C}_t^* + \widehat{I}_t^* + \widehat{G}_t^* + \widehat{X}_t^* - \widehat{IM}_t^* \\ \widehat{Y}_t^* & = 10 + 0.8(\widehat{Y}_t^* - \widehat{T}_t^*) + \widehat{I}_t^* + \widehat{G}_t^* + 0.3\widehat{Y}_t - 0.3\widehat{Y}_t^* \\ \widehat{Y}_t^* & = 22 + 0.8\widehat{Y}_t^* - 0.3\widehat{Y}_t^* + 0.3\widehat{Y}_t \\ \widehat{Y}_t^* & = \frac{1}{1 - 0.8 + 0.3}(22 + 0.3\widehat{Y}_t) \\ \widehat{Y}_t^* & = 44 + 0.6\widehat{Y}_t \end{split}\] Where \(\frac{1}{1 - 0.8 + 0.3} = \frac{1}{0.5} = 2 > 1\) is the multiplier for the foreign economy without taking into account the effect of the GDP of the national economy.
\[\begin{split} \widehat{Y}_t & = 44 + 0.6(44 + 0.6\widehat{Y}_t) \\ 0.64\widehat{Y}_t & = 70.4 \\ \widehat{Y}_t & = 110 \end{split}\]
Also we have that \(\widehat{Y}_t^* = 44 + 0.6*110 = 110\) so \(\widehat{Y}_t = \widehat{Y}_t^* = 110\).
In the case of the multiplier because \(\widehat{Y}_t = \frac{1}{1 - 0.8 + 0.3}(22 + 0.3\widehat{Y}_t^*)\) then:
\[\begin{split} \widehat{Y}_t & = \frac{1}{1 - 0.8 + 0.3}(22 + 0.3(44 + 0.6\widehat{Y}_t)) \\ \widehat{Y}_t & = \frac{1}{1 - 0.8 + 0.3}(22 + 0.3(44)) + \frac{0.3*0.6}{1 - 0.8 + 0.3}\widehat{Y}_t \\ \frac{1 - 0.8 + 0.3 - 0.3*0.6}{1 - 0.8 + 0.3}\widehat{Y}_t & = \frac{1}{1 - 0.8 + 0.3}(22 + 0.3(44)) \\ \widehat{Y}_t & = \frac{1}{1 - 0.8 + 0.3 - 0.3*0.6}(22 + 0.3(44)) \end{split}\]
Where \(5 > \frac{1}{1 - 0.8 + 0.3 - 0.3*0.6} = \frac{1}{0.32} = 3.125 > 2\) is the multiplier for the domestic economy taking into account the effect of the GDP of the foreign economy. Also because \(\widehat{Y}_t = \widehat{Y}_t^*\) this value is the multiplier for the foreign economy taking into account the effect of the GDP of the domestic economy.
If \(\widehat{Y}_t = 125\) then \(\widehat{Y}_t^* = 44 + 0.6*125 = 119\).
Also \(\widehat{Y}_t = 10 + 0.8(\widehat{Y}_t - 10) + 10 + \widehat{G}_t + 0.3\widehat{Y}_t^* - 0.3\widehat{Y}_t\) because the domestic government want to change the value of \(\widehat{G}_t\) we have that:
\(125 = 10 + 0.8(125 - 10) + 10 + \widehat{G}_t + 0.3*119 - 0.3*125\). Therefore:
For the domestic economy we have \(\widehat{T}_t - \widehat{G}_t = 10 - 14.8 = -4.8\) and \(\widehat{NX}_t = 0.3*119 - 0.3*125 = -1.8\). These situations generate a budget deficit and a trade deficit in the domestic economy as is explained in Oliver Blanchard (2017) Macroeconomics (7 Edition) > Chapter 3 The Goods Market.
For the foreign economy we have \(\widehat{T}_t - \widehat{G}_t = 10 - 10 = 0\) and \(\widehat{NX}_t = 0.3*125 - 0.3*119 = 1.8\).
If \(\widehat{Y}_t = \widehat{Y}_t^* = 125\), because the domestic and foreign governments are committed to increase government spending by the same amount and \(\widehat{Y}_t = 10 + 0.8(\widehat{Y}_t - 10) + 10 + \widehat{G}_t + 0.3\widehat{Y}_t^* - 0.3\widehat{Y}_t\) then:
\(125 = 10 + 0.8(125 - 10) + 10 + \widehat{G}_t + 0.3*125 - 0.3*125\). Therefore:
For the domestic and foreign economies we have \(\widehat{T}_t - \widehat{G}_t = \widehat{T}_t^* - \widehat{G}_t^* = 10 - 13 = -3\) and \(\widehat{NX}_t = \widehat{NX}_t^* = 0.3*125 - 0.3*125 = 0\). These situations generate only a budget deficit in both economies.
The data of the table was taken from https://github.com/TheEconomist/big-mac-data↩︎